Poission equation, spherical harmonics, looking for reference

[Derivator]

Hi folks,

I'm looking for a derivation of the following statement (formula 76)
http://img845.imageshack.us/img845/1550/screenshot4op.png

Do you know any reference, where I can find a bit more detailed description? I reckon, you can find it in Jackson's electrodynamic book, but I couldn't find it.derivator

 

[Polyrhythmic]

Well, if you take a look at the original definition of the electrostatic potential, which is basically given by something proportional to q/|r-r'|. In order to get q, you have to integrate over the charge density rho which is given in your text. The factor of 1/|r-r'| is also given there, so you just have to combine those two and calculate.

 

[Meir Achuz]

Try Sec. 4.2.5 in Franklin "Classical Electromagnetism".

 

[Studiot]

Weinberger "A first Course in Partial Differential Equations" treats this in his chapter on Legendre and associated functions p 192 ff

But any good book on partial diffs should have a similar treatment.